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A softball pitcher winds up and spins her arm around before releasing the ball. The pitcher's shoulders are 1.35m tall and arm is 0.36m long. The pitcher can spin her arm 15 revolutions every 2 seconds and at t = 0 her hand is it it's maximum height.

 

A) Determine an sinusoidal equation to represent the height of the pitchers hand.

 

B) Determine the height of the pitchers hand at t = 0.1 seconds

 Dec 11, 2019
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A softball pitcher winds up and spins her arm around before releasing the ball. The pitcher's shoulders are 1.35m tall and arm is 0.36m long. The pitcher can spin her arm 15 revolutions every 2 seconds and at t = 0 her hand is it it's maximum height.

 

A) Determine an sinusoidal equation to represent the height of the pitchers hand.

 

B) Determine the height of the pitchers hand at t = 0.1 seconds

 

Here is the equation.

 

\(\displaystyle h=Asin[2\pi f(t-p)]+v \)

 

h is height in metres

t is time in seconds

 

A is the amplitude                                                 A=0.36

v is the vertical shift                                               v= 1.35

f is the frequency which is  cycles/second            f=15/2

p is horizontal phase shift.  

    Here there are  2seconds per 15revolutions.  

     the phase shift is a quarter of that in a negative direction.  So p= -1/30

 

so

\(h= 0.36sin[2\pi*\frac{15}{2}(t+\frac{1}{30})]+1.35\\ h= 0.36sin[15\pi(t+\frac{1}{30})]+1.35\\\)

                 

Here is the graph

 

Now you can check my working and answer the substitution questions yourself.

 Dec 11, 2019

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